What is the derivative of f(x)= 1/(sqrt(x^3)) ?

The derivative of f(x)= 1/(sqrt(x^3)) is -(3x^2)/(2(x^3)^{3/2)}

What is the first derivative of f(x)= 1/(sqrt(x^3)) ?

The first derivative of f(x)= 1/(sqrt(x^3)) is -(3x^2)/(2(x^3)^{3/2)}

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derivative of

f (x) = \frac{1}{x ^{3}}

- \frac{3 x ^{2}}{2 ( x ^{3} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{3}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((x^{3})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{3})

= - \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= - \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \cdot 3 x^{2}

Simplify

- \frac{1}{2 ( x ^{3} ) ^{\frac{3}{2}}} \cdot 3 x^{2} : - \frac{3 x ^{2}}{2 ( x ^{3} ) ^{\frac{3}{2}}}

= - \frac{3 x ^{2}}{2 ( x ^{3} ) ^{\frac{3}{2}}}

f (x) = - \frac{10}{x}, at x = - 12

f (x) = x^{2} - 1

f (x) = \frac{1}{x ^{3}}

(- 1, 1)

f (x) = 9 x + 5, at x = 7

What is the derivative of f(x)= 1/(sqrt(x^3)) ?
The derivative of f(x)= 1/(sqrt(x^3)) is -(3x^2)/(2(x^3)^{3/2)}
What is the first derivative of f(x)= 1/(sqrt(x^3)) ?
The first derivative of f(x)= 1/(sqrt(x^3)) is -(3x^2)/(2(x^3)^{3/2)}